On images of locally finite derivations and E-derivations

Some cases of the LFED Conjecture, proposed by the second author [15], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions $k(x)$ of the polynomial algebra $k[x]$, the formal power series algebra $k[[x]]$ and the Laurent formal power series algebra $k[[x]][x^{?1}]$, where $x=(x_1,x_2,\dots ,x_n)$ denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized.     

A LOV2 Domain-Based Optogenetic Tool to Control Protein Degradation and Cellular Function

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Highlights? Optogenetic tool to control the stability of soluble and membrane proteins ? Engineered using the LOV2 domain and a murine ornithine decarboxylase-like degron ? Creation of light-switchable, conditional mutants ? Graded response to very low blue light intensities allows yeast photography     

Loss of ferromagnetism in YNi3 after H2 absorption

The compound YNi₃ ($\text{PuNi}{}_3\text{-}\text{type}\text{,}\text{a}\text{= 4.973}\text{A}\text{?}\text{,}\text{c}\text{= 24.42}\text{A}\text{?}$) is ferromagnetic below T_c = 35 K. After hydrogen absorption it loses its ferromagnetic character and becomes Pauli paramagnetic. The composition of the ternary hydride is approximately YNi₃H₄. The lattice constants are $\text{a}\text{= 5.267}\text{A}\text{?}$, $\text{c}\text{= 26.57}\text{A}\text{?}$.     

Coordinates in two variables over a -algebra

This paper studies coordinates in two variables over a -algebra. It gives several ways to characterize such coordinates. Also, various results about coordinates in two variables that were previously only known for fields, are extended to arbitrary -algebras.

     

Images of locally finite derivations of polynomial algebras in two variables

In this paper we show that the image of any locally finite k-derivation of the polynomial algebra k[x,y] in two variables over a field k of characteristic zero is a Mathieu subspace. We also show that the two-dimensional Jacobian conjecture is equivalent to the statement that the image of every k-derivation D of k[x,y] such that and is a Mathieu subspace of k[x,y].     

On the structure and dynamics of duplex GNA

Glycol nucleic acid (GNA), with a nucleotide backbone comprising of just three carbons and the stereocenter derived from propylene glycol (1,2-propanediol), is a structural analog of nucleic acids with intriguing biophysical properties, such as formation of highly stable antiparallel duplexes with high Watson-Crick base pairing fidelity. Previous crystallographic studies of double stranded GNA (dsGNA) indicated two forms of backbone conformations, an elongated M-type (containing metallo-base pairs) and the condensed N-type (containing brominated base pairs). A herein presented new crystal structure of a GNA duplex at 1.8 ? resolution from self-complementary 3'-CTC(Br)UAGAG-2' GNA oligonucleotides reveals an N-type conformation with alternating gauche-anti torsions along its (O3'-C3'-C2'-O2') backbone. To elucidate the conformational state of dsGNA in solution, molecular dynamic simulations over a period of 20 ns were performed with the now available repertoire of structural information. Interestingly, dsGNA adopts conformational states in solution intermediate between experimentally observed backbone conformations: simulated dsGNA shows the all-gauche conformation characteristic of M-type GNA with the higher helical twist common to N-type GNA structures. The so far counterintuitive, smaller loss of entropy upon duplex formation as compared to DNA can be traced back to the conformational flexibility inherent to dsGNA but missing in dsDNA. Besides extensive interstrand base stacking and conformational preorganization of single strands, this flexibility contributes to the extraordinary thermal stability of GNA.